Initialize
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Tools≻Load Package:
Student Multivariate Calculus
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Loading Student:-MultivariateCalculus
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Context Panel: Assign Name
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Access the MultiInt command via the Context Panel
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Write , the name of the integrand.
Context Panel: Evaluate and Display Inline
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Context Panel: Student Multivariate Calculus≻Integrate≻Iterated
Fill in both panes (see Figures 5.3.(1, 2)) and select "integral" for the Output
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Context Panel: Evaluate Integral
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Table 5.3.10(a) illustrates the visualization task template wherein a double integral can be iterated in the order . In the drop-down for area-element , select the ordering for the iteration. Then fill in the remaining fields as shown. The display in the table shows the end-state of the task template. To re-initialize it so that, for example, the buttons under "Value of Integral" work, re-select the Area Element. (If one of these buttons is pressed first, the Area Element will reset to "Select dA.")
Tools≻Tasks≻Browse:
Calculus - Multivariate≻Integration≻Visualizing Regions of Integration≻
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Evaluate and Graph
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Area Element
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Value of Integral
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Table 5.3.10(a) Visualizing and the resulting volume for iteration in the order
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The vertical arrow in the left-hand graph indicates that the iteration is in the order , whereby the first (or inner) integration is in the vertical direction, from the lowermost boundary curve to the uppermost. Because the integrand is positive, the double integral calculates the volume below the surface but above the plane . The solid whose volume is thereby calculated is seen in the right-hand graph.
The detailed analytic results below are obtained via the palettes and Context Panel.
Iterate and
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Calculus palette:
Template for definite iterated double integral
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Context Panel: Evaluate and Display Inline
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Display the iterated integrals
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Calculus palette:
Template for definite iterated double integral
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Context Panel:
2-D Math≻Convert To≻Inert Form
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Context Panel: Evaluate Integral
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